메뉴 건너뛰기




Volumn 27, Issue 6, 2006, Pages 1803-1816

Computational study of fast methods for the eikonal equation

Author keywords

Eikonal; Fast marching; Fast sweeping; Hamilton Jacobi; Viscosity solution

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY; COMPUTATIONAL METHODS; NONLINEAR EQUATIONS; PROBLEM SOLVING;

EID: 33751231737     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/040605655     Document Type: Article
Times cited : (55)

References (19)
  • 1
    • 0030521036 scopus 로고    scopus 로고
    • Numerical discretization of the first order Hamilton-Jacobi equations on triangular meshes
    • R. ABGRALL, Numerical discretization of the first order Hamilton-Jacobi equations on triangular meshes, Comm. Pure Appl. Math., 49 (1996), pp. 1339-1377.
    • (1996) Comm. Pure Appl. Math. , vol.49 , pp. 1339-1377
    • Abgrall, R.1
  • 3
    • 33846385358 scopus 로고
    • Thanks, heaps
    • J. BENTLEY, Thanks, heaps, Comm. ACM, 28 (1985), pp. 245-250.
    • (1985) Comm. ACM , vol.28 , pp. 245-250
    • Bentley, J.1
  • 4
    • 0001678817 scopus 로고    scopus 로고
    • Markov chain approximations for deterministic control problems with affine dynamics and quadratic cost in the control
    • M. BOUÉ AND P. DUPUIS, Markov chain approximations for deterministic control problems with affine dynamics and quadratic cost in the control, SIAM J. Numer. Anal., 36 (1999), pp. 667-695.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 667-695
    • Boué, M.1    Dupuis, P.2
  • 5
    • 84968507121 scopus 로고
    • Some properties of viscosity solutions of Hamilton-Jacobi equations
    • M. CRANDALL, L. EVANS, AND P.-L. LIONS, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., 282 (1984), pp, 487-502.
    • (1984) Trans. Amer. Math. Soc. , vol.282 , pp. 487-502
    • Crandall, M.1    Evans, L.2    Lions, P.-L.3
  • 6
    • 84966245867 scopus 로고
    • Two approximations of solutions of Hamilton- Jacobi equations
    • M. CRANDALL AND P.-L. LIONS, Two approximations of solutions of Hamilton- Jacobi equations, Math. Comp., 43 (1984), pp. 1-19.
    • (1984) Math. Comp. , vol.43 , pp. 1-19
    • Crandall, M.1    Lions, P.-L.2
  • 7
    • 0033296133 scopus 로고    scopus 로고
    • A discontinuous Galerkin method for Hamilton-Jacobi equations
    • G. HU AND C.-W. SHU, A discontinuous Galerkin method for Hamilton-Jacobi equations, SIAM J. Sci. Comput., 21 (1999), pp. 666-690.
    • (1999) SIAM J. Sci. Comput. , vol.21 , pp. 666-690
    • Hu, G.1    Shu, C.-W.2
  • 8
    • 1942507479 scopus 로고    scopus 로고
    • Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations, 3
    • C.-Y. KAO, S. OSHER, AND J. QIAN, Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations, 3. Comput. Phys., 196 (2004), pp. 367-391.
    • (2004) Comput. Phys. , vol.196 , pp. 367-391
    • Kao, C.-Y.1    Osher, S.2    Qian, J.3
  • 9
    • 0033443186 scopus 로고    scopus 로고
    • Finite volume schemes for Hamilton-Jacobi equations
    • G. KOSSIORIS, C. MAKRIDAKIS, AND P. SOUGANIDIS, Finite volume schemes for Hamilton-Jacobi equations, Numer. Math., 83 (1999), pp. 427-442.
    • (1999) Numer. Math. , vol.83 , pp. 427-442
    • Kossioris, G.1    Makridakis, C.2    Souganidis, P.3
  • 10
    • 0026204106 scopus 로고
    • High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations
    • S. OSHER AND C.-W. SHU, High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations, SIAM J. Numer. Anal., 28 (1991), pp. 907-922.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 907-922
    • Osher, S.1    Shu, C.-W.2
  • 11
    • 0036179755 scopus 로고    scopus 로고
    • An adaptive finite difference method for traveltimes and amplitudes
    • J. QIAN AND W.W. SYMES, An adaptive finite difference method for traveltimes and amplitudes, Geophysics, 67 (2002), pp. 167-176.
    • (2002) Geophysics , vol.67 , pp. 167-176
    • Qian, J.1    Symes, W.W.2
  • 12
    • 0026880997 scopus 로고
    • A viscosity solutions approach to shape-from-shading
    • E. ROUY AND A. TOURIN, A viscosity solutions approach to shape-from-shading, SIAM J. Numer. Anal., 29 (1992), pp. 867-884.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 867-884
    • Rouy, E.1    Tourin, A.2
  • 13
    • 0032631799 scopus 로고    scopus 로고
    • Fast marching methods
    • J.A. SETHIAN, Fast marching methods, SIAM Rev., 41 (1999), pp. 199-235.
    • (1999) SIAM Rev. , vol.41 , pp. 199-235
    • Sethian, J.A.1
  • 14
    • 0034705102 scopus 로고    scopus 로고
    • Fast methods for the Eikonal and related Hamilton-Jacobi equations on unstructured meshes
    • J.A. SETHIAN AND A. VLADIMIRSKY, Fast methods for the Eikonal and related Hamilton-Jacobi equations on unstructured meshes, Proc. Natl. Acad. Sci. USA, 97 (2000), pp. 5699-5703.
    • (2000) Proc. Natl. Acad. Sci. USA , vol.97 , pp. 5699-5703
    • Sethian, J.A.1    Vladimirsky, A.2
  • 15
    • 1842511489 scopus 로고    scopus 로고
    • Ordered upwind methods for static Hamilton-Jacobi equations: Theory and algorithms
    • J.A. SETHIAN AND A. VLADIMIRSKY, Ordered upwind methods for static Hamilton-Jacobi equations: Theory and algorithms, SIAM J. Numer. Anal., 41 (2003), pp. 325-363.
    • (2003) SIAM J. Numer. Anal. , vol.41 , pp. 325-363
    • Sethian, J.A.1    Vladimirsky, A.2
  • 16
    • 1942479348 scopus 로고    scopus 로고
    • Fast sweeping algorithms for a class of Hamilton-Jacobi problems
    • Y.H.R. TSAI, L.T. CHENG, S. OSHER, AND H.K. ZHAO, Fast sweeping algorithms for a class of Hamilton-Jacobi problems, SIAM J. Numer. Anal., 41 (2003), pp. 673-694.
    • (2003) SIAM J. Numer. Anal. , vol.41 , pp. 673-694
    • Tsai, Y.H.R.1    Cheng, L.T.2    Osher, S.3    Zhao, H.K.4
  • 17
    • 0029373106 scopus 로고
    • Efficient algorithms for globally optimal trajectories
    • J.N. TSITSIKLIS, Efficient algorithms for globally optimal trajectories, IEEE Trans. Automat. Control, 40 (1995), pp. 1528-1538.
    • (1995) IEEE Trans. Automat. Control , vol.40 , pp. 1528-1538
    • Tsitsiklis, J.N.1
  • 18
    • 0000890375 scopus 로고
    • Heapsort
    • J.W.J WILLIAMS, Heapsort, Comm. ACM, 7 (1964), pp. 347-348.
    • (1964) Comm. ACM , vol.7 , pp. 347-348
    • Williams, J.W.J.1
  • 19
    • 14944383149 scopus 로고    scopus 로고
    • Fast sweeping method for eikonal equations
    • H.K. ZHAO, Fast sweeping method for eikonal equations, Math. Comp., 74 (2005), pp. 603-627.
    • (2005) Math. Comp. , vol.74 , pp. 603-627
    • Zhao, H.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.